On the torsion of Jacobians of principal modular curves of level 3^n Institutional Repository Document uri icon


  • We demonstrate that the 3-power torsion points of the Jacobians of the principal modular curves X(3^n) are fixed by the kernel of the canonical outer Galois representation of the pro-3 fundamental group of the projective line minus three points. The proof proceeds by demonstrating the curves in question satisfy a two-part criterion given by Anderson and Ihara. Two proofs of the second part of the criterion are provided; the first relies on a theorem of Shimura, while the second uses the moduli interpretation.

author list (cited authors)

  • Papanikolas, M., & Rasmussen, C.

complete list of authors

  • Papanikolas, Matthew||Rasmussen, Christopher

publication date

  • October 2005